1. Field of the Invention
The present invention relates to a technique for constructing a graph structure representing a tubular structure in a three-dimensional medical image.
2. Description of the Related Art
Lung cancers are a disease in which a survival rate sharply drops as the stage of the disease progresses. Therefore, early detection and early treatment of lung cancers are extremely important. For example, when a shadow of a suspicious tumor or the like is found in a simple X-ray image of a chest, a CT image or the like, precise examinations are necessary to judge whether the suspicious tumor is a tumor. If the suspicious tumor is a tumor, it is necessary to judge whether the tumor is benign or malignant. In judging whether the tumor is benign or malignant, a pathology examination is performed by removing a part of the tumor by a bronchial endoscope. In this examination, it is important to more speedily and more accurately move the endoscope to the position of the tumor. For that purpose, it is effective to recognize the shape (a branching pattern or the like) of bronchi and a path to the tumor by using a CT image obtained by imaging before the examination.
Here, a technique using a Hessian matrix has been proposed, as an image recognition technique for extracting linear structures, such as bronchi, from a three-dimensional medical image obtained by CT, or the like. Specifically, first, multi-resolution transformation is performed on the three-dimensional medical image. After then, eigenvalue analysis of Hessian matrix is performed on the image of each resolution to extract a linear structure element. The linear structure element has a characteristic that only one of three eigenvalues obtained by eigenvalue analysis is close to 0. Next, linear structure elements (blood vessels) in various sizes are extracted from the three-dimensional medical image by combining results of analyzing images of respective resolutions. Further, data of a tree structure representing tubular structures in the three-dimensional medical image are obtained by connecting the extracted linear structure elements to each other by using a minimum spanning tree algorithm. When the linear structure elements are connected to each other by the minimum spanning tree algorithm, a cost function based on a positional relationship between linear structure elements or the principal axis direction of each linear structure element represented by an eigenvector corresponding to the aforementioned eigenvalue close to 0 is used (Japanese Unexamined Patent Publication No. 2010-220742 (Patent Document 1).
Meanwhile, bronchi have a tree structure in which a diameter gradually becomes smaller from 20 mm or larger to 0.5 mm or less while repeating branching from a trachea, and exhibit different anatomical and image characteristics depending on the diameter. Specifically, first, the angle of branching is different. The angle of branching may be an obtuse angle at a large diameter portion of the bronchi, but the angle of branching is an acute angle at a small diameter portion of the bronchi. Second, the bronchi are interrupted. Specifically, the bronchi in an image are not interrupted at a large diameter portion of the bronchi as long as a stenosis caused by a disease or the like is not present. However, at a small diameter portion of the bronchi, the bronchi in the image may be represented as if the bronchi are interrupted because of a noise in the image, which is caused by a partial volume effect and a motion artifact of a heart. Third, the thickness of the wall of the bronchi is different. Specifically, since the wall of the bronchi is thick at a large diameter portion of the bronchi, a difference in CT values between the wall of the bronchi and an air region in the bronchi is prominent. However, since the wall of the bronchi is thin at a small diameter portion of the bronchi, a difference in CT values between the wall of the bronchi and the air region in the bronchi is small, and a boundary between the wall and the air region is vague.
When bronchi are extracted by using the technique disclosed in Patent Document 1, a minimum spanning tree algorithm is executed by using a cost function in which the principal axis direction of each linear structure element is considered. Therefore, even if an interruption in an image is present, or a difference between the wall of the bronchi and the air region in the image is small at a small diameter portion of the bronchi, it is possible to correctly connect each of the linear structure elements. However, in a part of the bronchi in which the diameter is large and the angle of branching is an obtuse angle, a difference between principal axis directions of neighboring linear structure elements is large. Therefore, there is a risk that the linear structure elements are not correctly connected to each other.